Magnetic resonance imaging (MRI) is an important diagnostic and imaging technique. MRI techniques are based on the absorption and emission of radio frequency (RF) energy by the nuclei of atoms. Typically, a target is placed in a strong magnetic field that causes the generally disordered and randomly oriented nuclear spins of the atoms to become aligned with the applied magnetic field. One or more RF pulses are transmitted into the target, perturbing the nuclear spins. As the nuclear spins relax to their aligned state, the nuclei emit RF energy that is detected by receiving coils disposed about the target. The received RF energy is processed into a magnetic resonance image of a portion of the target.
By utilizing non-uniform magnetic fields having gradients in each of three spatial dimensions, the location of the emitting nuclei can be spatially encoded so that the target can be imaged in three dimensions (3-D). The three dimensions are commonly two mutually orthogonal directions x and y defined in a plane denoted as a “slice” with a series of slices defined in a third mutually orthogonal direction z. As used herein, the x-direction is associated with a frequency-encoding (FE) direction, and the y-direction is associated with a phase-encoding (PE) direction. Generally, RF pulses having a range of frequencies are transmitted into the target, and through use of well-known frequency encoding (e.g., for the x-direction) and phase encoding techniques (e.g., for the y-direction), a set of MRI data is received by each of the receiver coils for each slice in the target.
MRI data provides a representation of the MRI image in the frequency domain, often called k-space domain, where kx, and ky are the spatial frequency variables in the x and y directions having units of cycles per unit distance. An image of the slice of the target is obtained by performing an inverse Fourier transformation of the k-space MRI data. In MRI systems having multiple receiver coils (parallel MRI), an image is reconstructed from each receiver coil, and a final image is a combination of the images from each coil. Multiple receiver coil systems can be used to achieve high spatial and temporal resolution, to suppress image artifacts, and to reduce MRI scan time.
MRI data can be acquired at the appropriate Nyquist sampling rate to avoid artifacts in the final image caused by aliasing. However, sampling at the Nyquist rate is time consuming, which can prevent the imaging of targets that move, such as a beating heart. To decrease scan time, parallel imaging can be used to exploit a difference in sensitivities between individual coil elements in a receiver array to reduce the total number of PE views that are acquired. A “view” constitutes all of the kx measurements for a single ky. For the simplest case, a reduction factor of two, the even or odd PE views are skipped relative to the fully sampled k-space.
Skipping every other line of k-space increases the distance of equidistantly sampled k-space lines. If the maximum ky is unchanged to maintain resolution, an aliased image may be generated from the k-space data. The reduction in the number of PE steps relative to the Nyquist sampling rate is known as undersampling and is characterized by a reduction factor, R. The various undersampling strategies can be divided into two groups, uniform undersampling and non-uniform undersampling. Uniform undersampling uses the equidistantly spaced distributed PE and causes aliasing in the reconstructed image. Non-uniform undersampling, also called variable-density undersampling, generally more densely samples a central region of k-space, and more sparsely samples an outer region. Parallel MRI (P-MRI) undersamples, as compared to the Nyquist sampling rate, by the reduction factor R, which may be 2 or more, to decrease the data acquisition time. The undersampling results in certain data in k-space not being acquired, and therefore not available for image reconstruction. However, dissimilarities in the spatial sensitivities of the multiple receiver coils provide supplementary spatial encoding information, which is known as “sensitivity encoding.” A fully sampled set of k-space MRI data can be produced by combining the undersampled, sensitivity-encoded MRI data received by different coils with reconstructed values for the unacquired data to create an image with removed aliasing artifacts.
Coil sensitivities can be used to reconstruct the full-FOV image in the image space domain or in the k-space domain as known to those skilled in the art. In sensitivity encoding (SENSE) reconstruction, coil sensitivity estimates determined from reference scans are applied to reconstruct images from subsequent scans in the image space domain. It is well known that SENSE reconstruction is artifactual when coil sensitivity estimates deviate from the true coil sensitivities due to subject or coil motion between reference and imaging scans. This high sensitivity to error in coil sensitivity estimates is caused by the local nature of SENSE reconstruction. In the conventional SENSE with data sampling on a regular Cartesian grid, reconstruction (de-aliasing) is done independently for each spatial location in the aliased image using local reconstruction coefficients defined by the coil sensitivity values at the corresponding spatial locations.
The scenario is very different for parallel MRI reconstruction techniques such as generalized autocalibrating partially parallel acquisition (GRAPPA) and generalized autocalibrating reconstruction for sensitivity encoded MRI (GARSE) which operate in the k-space domain. These methods utilize only correlations between closely situated k-space locations. Therefore, only low frequency descriptors of coil sensitivities are essential for these methods. Because of the low resolution (low frequency) nature of these descriptors, they can be noticeably altered only by a substantial change in coil or imaged object position. Thus, k-space domain methods for parallel MRI such as GRAPPA and GARSE are less sensitive to motion between reference and imaging scans than SENSE-like techniques.
In GRAPPA, acquired samples in the k-space locations closest to the missing k-space position in the PE direction are used to estimate the value of the missing sample. Such an approach is only optimal when the coil sensitivities can be described by slowly varying functions in image space dependent only on the y-coordinate (PE direction). For real coils used in MRI studies, coil sensitivities are spatially variable in all directions. Thus, GRAPPA provides quality results for low reduction factors, but is less applicable for high reduction factors due to residual aliasing artifacts and substantial noise amplification in the reconstructed images. What is needed, therefore, is a method and a system for parallel reconstruction in the k-space domain which supports high reduction factors and lower noise and artifact levels as compared to existing methods.